# 6.4 Solve simple interest applications

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By the end of this section, you will be able to:
• Use the simple interest formula
• Solve simple interest applications

Before you get started, take this readiness quiz.

1. Solve $0.6y=45.$
If you missed this problem, review Decimals and Fractions .
2. Solve $\frac{n}{1.45}=4.6.$
If you missed this problem, review Decimals and Fractions .

## Use the simple interest formula

Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal , $P,$ and the bank pays you interest , $I.$ The interest is computed as a certain percent of the principal; called the rate of interest , $r.$ The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, $t,$ represents the number of years the money is left in the account.

## Simple interest

If an amount of money, $P,$ the principal, is invested for a period of $t$ years at an annual interest rate $r,$ the amount of interest, $I,$ earned is

$I=Prt\phantom{\rule{2em}{0ex}}$

where

$\begin{array}{ccc}\hfill I& =& \text{interest}\hfill \\ \hfill P& =& \text{principal}\hfill \\ \hfill r& =& \text{rate}\hfill \\ \hfill t& =& \text{time}\hfill \end{array}$

Interest earned according to this formula is called simple interest    .

The formula we use to calculate simple interest is $I=Prt.$ To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

Find the simple interest earned after $3$ years on $\text{500}$ at an interest rate of $\text{6%.}$

## Solution

Organize the given information in a list.

$\begin{array}{ccc}\hfill I& =& ?\hfill \\ \hfill P& =& \text{500}\hfill \\ \hfill r& =& \text{6%}\hfill \\ \hfill t& =& \text{3 years}\hfill \end{array}$

We will use the simple interest formula to find the interest.

 Write the formula. $I=Prt$ Substitute the given information. Remember to write the percent in decimal form. $I=\left(500\right)\left(0.06\right)\left(3\right)$ Simplify. $I=90$ Check your answer. Is $90 a reasonable interest earned on$500 in 3 years? In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes,$90 is reasonable. Write a complete sentence that answers the question. The simple interest is $90. Find the simple interest earned after $4$ years on $\text{800}$ at an interest rate of $\text{5%.}$$160

Find the simple interest earned after $2$ years on $\text{700}$ at an interest rate of $\text{4%.}$

$56 In the next example, we will use the simple interest formula to find the principal. Find the principal invested if $\text{178}$ interest was earned in $2$ years at an interest rate of $\text{4%.}$ ## Solution Organize the given information in a list. $\begin{array}{ccc}\hfill I& =& \text{178}\hfill \\ \hfill P& =& ?\hfill \\ \hfill r& =& \text{4%}\hfill \\ \hfill t& =& \text{2 years}\hfill \end{array}$ We will use the simple interest formula to find the principal.  Write the formula. $I=Prt$ Substitute the given information. $178=P\left(0.04\right)\left(2\right)$ Divide. $\frac{178}{0.08}=\frac{0.08P}{0.08}$ Simplify. $2,225=P$ Check your answer. Is it reasonable that$2,225 would earn $178 in 2 years? $I=Prt$ $178\stackrel{?}{=}2,225\left(0.04\right)\left(2\right)$ $178=178✓$ Write a complete sentence that answers the question. The principal is$2,225.

Find the principal invested if $\text{495}$ interest was earned in $3$ years at an interest rate of $\text{6%.}$

$2,750 Find the principal invested if $\text{1,246}$ interest was earned in $5$ years at an interest rate of $\text{7%}.$$3,560

Now we will solve for the rate of interest.

Find the rate if a principal of $\text{8,200}$ earned $\text{3,772}$ interest in $4$ years.

## Solution

Organize the given information.

$\begin{array}{ccc}\hfill I& =& \text{3,772}\hfill \\ \hfill P& =& \text{8,200}\hfill \\ \hfill r& =& ?\hfill \\ \hfill t& =& \text{4 years}\hfill \end{array}$

We will use the simple interest formula to find the rate.

 Write the formula. $I=Prt$ Substitute the given information. $3,772=8,200r\left(4\right)$ Multiply. $3,772=32,800r$ Divide. $\frac{3,772}{32,800}=\frac{32,800r}{32,800}$ Simplify. $0.115=r$ Write as a percent. $\text{11.5%}=r$ Check your answer. Is 11.5% a reasonable rate if $3,772 was earned in 4 years? $I=Prt$ $3,772\stackrel{?}{=}8,200\left(0.115\right)\left(4\right)$ $3,772=3,772✓$ Write a complete sentence that answers the question. The rate was 11.5%. #### Questions & Answers how can chip be made from sand Eke Reply are nano particles real Missy Reply yeah Joseph Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master? Lale Reply no can't Lohitha where we get a research paper on Nano chemistry....? Maira Reply nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review Ali what are the products of Nano chemistry? Maira Reply There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others.. learn Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level learn Google da no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts Bhagvanji hey Giriraj Preparation and Applications of Nanomaterial for Drug Delivery Hafiz Reply revolt da Application of nanotechnology in medicine has a lot of application modern world Kamaluddeen yes narayan what is variations in raman spectra for nanomaterials Jyoti Reply ya I also want to know the raman spectra Bhagvanji I only see partial conversation and what's the question here! Crow Reply what about nanotechnology for water purification RAW Reply please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment. Damian yes that's correct Professor I think Professor Nasa has use it in the 60's, copper as water purification in the moon travel. Alexandre nanocopper obvius Alexandre what is the stm Brian Reply is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.? Rafiq industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong Damian How we are making nano material? LITNING Reply what is a peer LITNING Reply What is meant by 'nano scale'? LITNING Reply What is STMs full form? LITNING scanning tunneling microscope Sahil how nano science is used for hydrophobicity Santosh Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq Rafiq what is differents between GO and RGO? Mahi what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq Rafiq if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION Anam analytical skills graphene is prepared to kill any type viruses . Anam Any one who tell me about Preparation and application of Nanomaterial for drug Delivery Hafiz what is Nano technology ? Bob Reply write examples of Nano molecule? Bob The nanotechnology is as new science, to scale nanometric brayan nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale Damian A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place. Kimberly Reply Jeannette has$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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